Dovizioso got the perfect launch from P1 as Johann Zarco (Monster Yamaha Tech 3) and Jack Miller (Alma Pramac Racing) just came into contact off the front row.
Marquez, meanwhile, kept the inside line from P6 to get himself into P3 before dispatching Miller at Turn 9 for P2 - and Dovi's qualifying advantage had disappeared after just half a lap.
Crutchlow then got past Miller to latch onto Marquez and Dovi, with Valentino Rossi (Movistar Yamaha MotoGP) making a great start from P9 to get himself up to fourth as he passed Miller into Turn 11.
The three at the front then put the hammer down as Dovizioso slammed in a 1:45.7 on Lap 6 though, and Crutchlow and Marquez kept tabs on the Italian but fourth place Rossi suddenly found himself over eight tenths back.
The pace was fluctuating but the leading trio started to edge away from the nine-time world champion bit by bit, who in turn had two Team Suzuki Ecstar riders homing in on him.
With eight laps to go, Dovizioso and Marquez exchanged 1:45s with Crutchlow a whisper behind but a lap later the number 35 was two tenths slower as the front two started to make the decisive break. Dovi's intent was clear: a fastest lap of the race, hammer firmly down and the pin pulled.
It was, Dovizioso vs Marquez on the final five laps. Marquez sat behind the Desmosedici before making a move into P1 at Turn 9 - no immediate reply for Dovi. With three to go the Ducati was swarming, but there was no way past with two to go.
Then, a huge moment and one that decided the 2018 title. Pushing hard to keep with Marquez, Dovi tucked the front of his GP18 at Turn 10 with just over two laps to go, crashing out of the race to leave Marquez with a healthy margin to Crutchlow and Rins.
Pushing to the limit to deny the Spaniard the Italian found that limit and just stepped over it, and Marquez was left chasing the crown in clear air.
Crutchlow held off Rins for P2 at the line, with Rins less than two tenths behind the British rider to secure a phenomenal home podium for Suzuki.